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Chaos-induced enhancement of resonant multielectron recombination in highly charged ions: Statistical theory

A statistical theory of resonant multielectron recombination based on properties of chaotic eigenstates is developed. The level density of many-body states increases exponentially with the number of excited electrons. When the residual electron-electron interaction exceeds the interval between these levels, the eigenstates (called compound states or compound resonances if these states are in the continuum) become "chaotic" superpositions of large numbers of Hartree-Fock configurational basis states. This situation takes place in some rare-earth atoms and many open-shell multiply charged ions excited in the process of electron recombination. Our theory describes resonant multielectron recombination via dielectronic doorway states leading to such compound resonances. The result is a radiative capture cross section averaged over a small energy interval containing several compound resonances. In many cases individual resonances are not resolved experimentally (since the interval between them is small, e.g., $\le 1$ meV, possibly even smaller than their radiative widths), therefore, our statistical theory should correctly describe the experimental data. We perform numerical calculations of the recombination cross sections for tungsten ions W$^{q+}$, $q=18$--25. The recombination rate for W$^{20+}$ measured recently [Phys. Rev. A {\bf 83}, 012711 (2011)] is $10^3$ greater than the direct radiative recombination rate at low energies, and our result for W$^{20+}$ agrees with the measurements.